Difference between revisions of "B(x,y)=integral (t^(x-1)+t^(y-1))(1+t)^(-x-y) dt"
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==References== | ==References== | ||
| − | * {{BookReference|Higher Transcendental Functions Volume I|1953| | + | * {{BookReference|Higher Transcendental Functions Volume I|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=Beta as improper integral|next=Beta is symmetric}}: $\S 1.5 (3)$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 20:57, 3 March 2018
Theorem
The following formula holds: $$B(x,y) = \displaystyle\int_0^1 (t^{x-1}+t^{y-1})(1+t)^{-x-y} \mathrm{d}t,$$ where $B$ denotes the beta function.
Proof
References
- 1953: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 1.5 (3)$
